The four line-based Pareto fronts considered in this section are not so realistic. They can be hardly found in real-world applications. However, as shown in [1]}, when the reference point is sufficiently far away, the solutions for hypervolume maximization are distributed on the boundary of some realistic Pareto fronts (e.g., the Pareto fronts of DTLZ1\(^{-1}\)  [2]} and WFG3 [3]}). In this case, it is meaningful to investigate the hypervolume optimal \(\mu \) -distribution on the line-based Pareto fronts since the line-based Pareto fronts can be viewed as the boundary of some realistic Pareto fronts. This is the main motivation to investigate the line-based Pareto fronts.
